I live in US and want to travel to Cuba with my Chilean passport

Maybe my personal experience travelling to Cuba can be useful here.

My family and I (wife and toddler) are US citizens holding only US passports. We went to Cuba in July, after the new restrictions were announced but before they were implemented. We checked in at the airport separately (I was meeting her there from work) and while they asked my wife to identify which of the 12 reasons for going applied to her, no one, neither in the US nor in Cuba, asked me for my reason. When we returned back to the US we simply walked in, showed the CBP officer our passports (with the Cuban entry stamp, which is optional) and he waved us right through. He couldn't have cared less why we went (or even where).

Hence, my advice would be to just use your US passport, go to "Support the Cuban People" by staying in privately-owned homes or hotels and dining at privately-owned restaurants and avoiding playing the authorities. Unless things have really changed since July they won't care at all. Can anyone who has visited more recently chime in here?

It sounds like you are not intending to get the required license from the US Dept. Of Treasury prior to your trip and some how want to sidestep the issue by playing sleight of hand with your two passports. This will most likely end up very bad for you no matter how you do it.

From the US State Dept. page on Cuba

Tourist travel to Cuba remains prohibited. You must obtain a license from the Department of Treasury or your travel must fall into one of 12 categories of authorized travel.

And

Travel to Cuba is regulated by the Office of Foreign Assets Control (OFAC) of the U.S. Department of the Treasury. Anyone located in the United States, regardless of citizenship and nationality, must comply with these regulations. Individuals seeking to travel to Cuba are not required to obtain licenses from OFAC if their travel is covered by a general license. If travel is not covered by a general license, you must seek OFAC authorization in the form of a specific license. Travelers who fail to comply with regulations may face penalties and criminal prosecution.

And from §515.560 Travel-related transactions to, from, and within Cuba by persons subject to U.S. jurisdiction. you can see the twelve words you can't say on TV categories approved for trips to Cuba, which are in summary

1. Family visits

2. Official business of the U.S. government, foreign governments, and certain intergovernmental organizations

3. Journalistic activity

4. Professional research and professional meetings

5. Educational activities

6. Religious activities

7. Public performances, clinics, workshops, athletic and other competitions, and exhibitions
8. Support for the Cuban people
9. Humanitarian projects
10. Activities of private foundations or research or educational institutes
11. Exportation, importation, or transmission of information or informational materials
12. Certain export transactions that may be considered for authorization under existing Department of Commerce regulations and guidelines with respect to Cuba or engaged in by U.S.-owned or -controlled foreign firms

While I love how they make the rules for the entire planet, you having a US passport makes it highly likely that they will come after you once they find out. And getting off a plane from Cuba and presenting your US passport will raise a huge flag to the authorities and you would end up answering a lot of embarrassing questions.

I would also not be surprised if the US authorities are in general watching flights to Cuba.